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Консультация № 199928
20.12.2020, 13:00
0.00 руб.
0
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1
Здравствуйте! У меня возникли сложности с таким вопросом:
Вычислить криволинейный интеграл первого рода
1┌
I = ──── │(10x - 18y + 2z - 3)dL , ,
___┘
√404 L
где L - отрезок, соединяющий точки
A(6,9,-5) ; B(4,-7,7)
Вычислить криволинейный интеграл первого рода
1┌
I = ──── │(10x - 18y + 2z - 3)dL , ,
___┘
√404 L
где L - отрезок, соединяющий точки
A(6,9,-5) ; B(4,-7,7)
Обсуждение
25.12.2020, 04:00
общий
это ответ
Здравствуйте, zhalykov.2015!
Если криволинейный интеграл первого рода вычисляется вдоль отрезка AB некоторой гладкой кривой, которая может быть задана параметрически в виде x = x(t), y = y(t), z = z(t), и при этом точкам A и B соответствуют значения параметра t[sub]A[/sub] и t[sub]B[/sub], то интеграл будет равен
В данном случае гладкая кривая представляет собой прямую, проходящую через точки A(6,9,-5) и B(4,-7,7), то есть имеющую направляющий вектор AB = {-2,-16,12}. Следовательно, её параметрическим уравнением будет x = 6-2t, y = 9-16t, z = 12t-5, причём точкам A и B соответствуют t[sub]A[/sub] = 0 и t[sub]B[/sub] = 1. Тогда интеграл будет равен
Если криволинейный интеграл первого рода вычисляется вдоль отрезка AB некоторой гладкой кривой, которая может быть задана параметрически в виде x = x(t), y = y(t), z = z(t), и при этом точкам A и B соответствуют значения параметра t[sub]A[/sub] и t[sub]B[/sub], то интеграл будет равен
В данном случае гладкая кривая представляет собой прямую, проходящую через точки A(6,9,-5) и B(4,-7,7), то есть имеющую направляющий вектор AB = {-2,-16,12}. Следовательно, её параметрическим уравнением будет x = 6-2t, y = 9-16t, z = 12t-5, причём точкам A и B соответствуют t[sub]A[/sub] = 0 и t[sub]B[/sub] = 1. Тогда интеграл будет равен
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